• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.5
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• pp.159-171
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• 2011

This paper suggests an algorithm that obtains the Minimum Spanning Tree for directed graph (DMST). The existing Chu-Liu/Edmonds DMST algorithm has chances of the algorithm not being able to find DMST or of the sum of ST not being the least. The suggested algorithm is made in such a way that it always finds DMST, rectifying the disadvantage of Chu-Liu/Edmonds DMST algorithm. Firstly, it chooses the Minimum-Weight Arc (MWA) from all the nodes including a root node, and gets rid of the nodes in which cycle occurs after sorting them in an ascending order. In this process, Minimum Spanning Forest (MST) is obtained. If there is only one MSF, DMST is obtained. And if there are more than 2 MSFs, to determine MWA among all MST nodes, it chooses a method of directly calculating the sum of all the weights, and hence simplifies the emendation process for solving a cycle problem of Chu-Liu/Edmonds DMST algorithm. The suggested Sulee DMST algorithm can always obtain DMST that minimizes the weight of the arcs no matter if the root node is set or not, and it is also capable to find the root node of a graph with minimized weight.

• The KIPS Transactions:PartA
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• v.17A no.3
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• pp.159-166
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• 2010

In this paper, to obtain the Minimum Spanning Tree (MST) from the graph with several nodes having the same weight, I applied both Bor$\dot{u}$vka and Kruskal MST algorithms. The result came out to such a way that Kruskal MST algorithm succeeded to obtain MST, but not did the Prim MST algorithm. It is also found that an algorithm that chooses Inter-MSF MWE in the $2^{nd}$ stage of Bor$\dot{u}$vka is quite complicating. The $1^{st}$ stage of Bor$\dot{u}$vka has an advantage of obtaining Minimum Spanning Forest (MSF) with the least number of the edges, and on the other hand, Kruskal MST algorithm has an advantage of always obtaining MST though it deals with all the edges. Therefore, this paper suggests an Hybrid MST algorithm which consists of the merits of both Bor$\dot{u}$vka's $1^{st}$ stage and Kruskal MST algorithm. When applied additionally to 6 graphs, Hybrid MST algorithm has a same effect as that of Kruskal MST algorithm. Also, comparing the algorithm performance speed and capacity, Hybrid MST algorithm has shown the greatest performance Therefore, the suggested algorithm can be used as the generalized MST algorithm.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.6
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• pp.165-173
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• 2012

Given a connected, weighted, and undirected graph, the Minimum Spanning Tree (MST) should have minimum sum of weights, connected all vertices, and without any cycle taking place. Borůvka Algorithm is firstly suggested as an algorithm to evaluate the MST, but it is not widely used rather than Prim and Kruskal algorithms. Borůvka algorithm selects the Minimum Weight Edge (MWE) from each vertex with distinct weights in $1^{st}$ stage, and selects the MWE from each MSF (Minimum Spanning Forest) in $2^{nd}$ stage. But the cycle check and the number of MSF in $1^{st}$ stage and $2^{nd}$ stage are difficult to implication by computer program even if it is easy to verify visually. This paper suggests the generalized Borůvka Algorithm, This algorithm selects all of the same MWEs for each vertex, then checks the cycle and constructs MSF for ascending sorted MWEs. Kruskal method bring into this process. if the number of MSF greats then 1, this algorithm selects MWE from ascending sorted inter-MSF edges. The generalized Borůvka algorithm is verified its application by being applied to the 7 graphs with the many minimum weights or distinct weight edges for any vertex. As a result, the generalized Borůvka algorithm is less required for cycle verification then the Kruskal algorithm. Therefore, the generalized Borůvka algorithm is more fast to obtain MST then Kruskal algorithm.